Many-particle projector

The many-particle projector rua is in this case fully described by the one-particle projector... 

If the many-particle projector ra undergoes the similarity transformation (3.18), the one-particle projector p undergoes the corresponding one-particle similarity transformation. 

We will describe, in some detail, one such modification, an effective Dirac equation (EDE) which was derived in a number of papers [7, 8, 9, 10]. This new equation is more convenient in many applications than the original BS equation, and we will derive some general formulae connected with this equation. The physical idea behind this approach is that in the case of a loosely bound system of two particles of different masses, the heavy particle spends almost all its life not far from its own mass shell. In such case some kind of Dirac equation for the light particle in an external Coulomb field should be an excellent starting point for the perturbation theory expansion. Then it is convenient to choose the free two-particle propagator in the form of the product of the heavy particle mass shell projector A and the free electron propagator... 

The effects of flow on the diffusion of particles suspended in a simple liquid is an important problem which was analyzed many times along the last 30 years. Several approaches have been followed in order to understand and quantify the effects of the presence of a velocity gradient on the diffusion coefficient D of the particles. Usually, these are restricted to the case of shear flow because this case is more manageable from the mathematical point of view, and because there are several experimental systems that allow the evaluation and validity of the corresponding results. The approaches followed vary from kinetic theory and projector operator techniques, to Langevin and Fokker-Planck equations. Here, we summarize some recent contributions to this subject and their results. 

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See also in sourсe #XX -- [ ]

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